Synchronization behavior of coupled neuron circuits composed of memristors

The fluctuation of intracellular and extracellular ion concentration induces the variation of membrane potential, and also complex distribution of electromagnetic field is generated. Furthermore, the membrane potential can be modulated by time-varying electromagnetic field. Therefore, magnetic flux is proposed to model the effect of electromagnetic induction in case of complex electrical activities of cell, and memristor is used to connect the coupling between membrane potential and magnetic flux. Based on the improved neuron model with electromagnetic induction being considered, the bidirectional coupling-induced synchronization behaviors between two coupled neurons are investigated on Spice tool and also printed circuit board. It is found that electromagnetic induction is helpful for discharge of neurons under positive feedback coupling, while electromagnetic induction is necessary to enhance synchronization behaviors of coupled neurons under negative feedback coupling. The frequency analysis on isolate neuron confirms that the frequency spectrum is enlarged under electromagnetic induction, and self-induction effect is detected. These experimental results can be helpful for further dynamical analysis on synchronization of neuronal network subjected to electromagnetic radiation.     

Cluster synchronization and rhythm dynamics in a complex neuronal network with chemical synapses

Cluster synchronization and rhythm dynamics are studied for a complex neuronal network with the small world structure connected by chemical synapses. Cluster synchronization is considered as that in-phase burst synchronization occurs inside each group of the network but diversity may take place among different groups. It is found that both one-cluster and multi-cluster synchronization may exist for chemically excitatory coupled neuronal networks, however, only multi-cluster synchronization can be achieved for chemically inhibitory coupled neuronal networks. The rhythm dynamics of bursting neurons can be described by a quantitative characteristic, the width factor. We also study the effects of coupling schemes, the intrinsic property of neurons and the network topology on the rhythm dynamics of the small world neuronal network. It is shown that the short bursting type is robust with respect to the coupling strength and the coupling scheme. As for the network topology, more links can only change the type of long bursting neurons, and short bursting neurons are also robust to the link numbers.     

生物神经网络系统动力学与功能研究

生物神经系统是由数量极其巨大的神经元相互联结的信息网络系统,在生物体的感觉、认知和运动控制中发挥关键性的作用.首先介绍神经元、大脑和一些生物神经网络的生理结构和理论模型,然后分别介绍其放电活动和网络动态特性的一些重要问题,包括神经元的复杂放电模式、耦合神经元网络系统的同步活动和时空动力学、大脑联合皮层神经微回路的网络结构特征,以及工作记忆和抉择过程的动力学机制等. 最后对今后研究给出一些展望.      

Machine learning of synaptic structure with neurons to promote tumor growth

In this paper, we use machine learning techniques to form a cancer cell model that displays the growth and promotion of synaptic and electrical signals. Here, such a technique can be applied directly to the spiking neural network of cancer cell synapses. The results show that machine learning techniques for the spiked network of cancer cell synapses have the powerful function of neuron models and potential supervisors for different implementations. The changes in the neural activity of tumor microenvironment caused by synaptic and electrical signals are described. It can be used to cancer cells and tumor training processes of neural networks to reproduce complex spatiotemporal dynamics and to mechanize the association of excitatory synaptic structures which are between tumors and neurons in the brain with complex human health behaviors.     

Chaotic dynamics in a neural network under electromagnetic radiation

In this paper, a small Hopfield neural network with three neurons is studied, in which one of the three neurons is considered to be exposed to electromagnetic radiation. The effect of electromagnetic radiation is modeled and considered as magnetic flux across membrane of the neuron, which contributes to the formation of membrane potential, and a feedback with a memristive type is used to describe coupling between magnetic flux and membrane potential. With the electromagnetic radiation being considered, the previous steady neural network can present abundant chaotic dynamics. It is found that hidden attractors can be observed in the neural network under different conditions. Moreover, periodic motion and chaotic motion appear intermittently with variations in some system parameters. Particularly, coexistence of periodic attractor, quasiperiodic attractor, and chaotic strange attractor, coexistence of bifurcation modes and transient chaos can be observed. In addition, an electric circuit of the neural network is implemented in Pspice, and the experimental results agree well with the numerical ones.     

Reproduce the biophysical function of chemical synapse by using a memristive synapse

Dynamical modeling of nervous systems is of fundamental importance in many scientific fields containing the topics relative to computational neuroscience and biophysics. Many feasible mathematical models have been suggested in the explanation and prediction of some features of neural activities. Considering the special experimental findings and the computational efficiency, it is necessary to find a perfect balance between estimating biophysical functions with complete dynamics and reducing complexity when a tractable model is built. In this paper, a chemical synaptic model is reproduced by using a memristive synapse because it not only remains synaptic characteristic but also exhibits a pinched hysteresis loop and active feature locally. That is, a neuron activated by chemical synapse can produce similar firing modes as the neuron coupled by a memristive synapse, and both the chemical synapse and memristive synapse have similar field effect and biophysical properties. By calculating the one-parameter and two-parameter bifurcation as well as the Lyapunov exponent spectrum, it is confirmed that a neuron can be excited by the chemical synapse or the memristive synapse for generating chaotic firing patterns. Oscillation of the circuit composed of neuron and functional synapse is analyzed, suggesting that there exists a relation between the local activity and the edge of chaos via Hopf bifurcation. A modular circuit is designed to construct large-scale neural network. These results in this paper provide new evidences for application of memristive components and guide us to know the biophysical function of chemical synapse from physical viewpoint, in which the chemical synapse could be a kind of memristive synapse because of the same biophysical function.

     

Experimental verification of a memristive neural network

This paper presents an electronic circuit able to emulate the behavior of a neural network based on memristive synapses. The latter is built with two flux-controlled floating memristor emulator circuits operating at high frequency and two passive resistors. Synapses are connected in a way that a bridge circuit is obtained, and its dynamical behavioral model is derived from characterizing memristive synapses. Analysis of the memristor characteristics for obtaining a suitable synaptic response is also described. A neural network of one neuron and two inputs is connected using the proposed topology, where synaptic positive and negative weights can easily be reconfigured. The behavior of the proposed artificial neural network based on memristors is verified through MATLAB, HSPICE simulations and experimental results. Synaptic multiplication is performed with positive and negative weights, and its behavior is also demonstrated through experimental results getting 6% of error.     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.     

Chaotic burst synchronization in heterogeneous small-world neuronal network with noise

Chaotic bursting is a fundamental behavior of neurons. In this paper, global and local burst synchronization is studied in a heterogeneous small-world neuronal network of non-identical Hindmarsh-Rose (HR) neurons with noise. It is found that the network can achieve global burst synchronization much more easily than phase synchronization and nearly complete synchronization. Moreover, local burst synchronized clusters have already formed before global burst synchronization happens. We study the effect of the shortcut-adding probability and the heterogeneity coefficient on local and global burst synchronization of the network and find that the introduction of shortcuts facilitates burst synchronization while the heterogeneity has little effect. Moreover, we study the spatiotemporal pattern of the network and find that there is an optimal coupling strength range in which the periodicity of the network is very apparent.     

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.     

Parameter-dependent synchronization of coupled neurons in cold receptor model

In this paper, synchronization in two coupled neurons with spiking, bursting and chaos firings is investigated as the coupling strength gets increased. Synchronization state can be identified by means of the bifurcation diagram, the correlation coefficient and ISI-distance. It is illustrated that the coupled neurons can exhibit different types of synchronization state when the coupling strength increases. The different synchronization processes appear similar, but their detailed processes are different depending on the parameter values. The synchronization of neuronal network with two different network connectivity patterns is also studied. It is shown that chaotic and high period pattern are more difficult to get complete synchronization than the situation in single spike and low period pattern. It is also demonstrated that the synchronization status of multiple neurons is dependent on the network connectivity patterns. These results may be instructive to understand synchronization in neuronal systems.     

Projective synchronization of nonlinear-coupled spatiotemporal chaotic systems

The projective synchronization of one-dimensional discrete spatiotemporal chaotic systems is discussed in this paper. The coupling equation is determined by suitably separating the linear term and the nonlinear term of the dynamic function, and two coupled map lattices reach projective synchronization by the nonlinear-coupling method. Besides, this method is expanded to the projective synchronization of the complex network composed by coupled map lattices. Numerical simulations show the effectiveness of the scheme.     

化学突触耦合神经元的簇放电同步

本文研究了经化学突触耦合的两个神经元的簇放电同步以及耦合后神经元的簇放电动力学性质.根据簇相位的定义,通过计算得到兴奋性耦合导致两个神经元达到同相簇放电同步,而抑制性耦合则使得两个神经元反相同步产生簇放电.本文给出了衡量单个神经元簇动力学的指标-宽度因子,根据此指标将簇放电模式分类为短簇和长簇两种,并且讨论了不同簇放电模式以及耦合方式对于耦合后神经元簇动力学性质的影响.结果表明兴奋性耦合有利于簇放电的整合,短簇的放电模式对于耦合作用具有鲁棒性.这一结果的研究对于将来神经实验中识别簇放电同步具有指导意义.     

Phase synchronization dynamics of coupled neurons with coupling phase in the electromagnetic field

Nonlinear Dynamics - Based on the law of electromagnetic theory, phase synchronization of coupled extended Hindmarsh–Rose neurons with magnetic and electrical couplings is discussed. It is...     

Firing synchronization of learning neuronal networks with small-world connectivity

The properties of firing synchronization of learning neuronal networks, electrically and chemically coupled ones, with small-world connectivity are studied. First, the variation properties of synaptic weights are examined. Next the effects of the synaptic learning rate on the properties of firing rate and synchronization are investigated. The influences of the coupling strength and the shortcut probability on synchronization are also explored. It is shown that synaptic learning suppresses over-excitement for the networks, helps synchronization for the electrically coupled neuronal network but destroys synchronization for the chemically coupled one. Both introducing shortcuts and increasing the coupling strength are helpful in improving synchronization of the neuronal networks. The spatio-temporal patterns illustrate and confirm the above results.     

Neurodynamics analysis of brain information transmission

This paper proposes a model of neural networks consisting of populations of perceptive neurons, inter-neurons, and motor neurons according to the theory of stochastic phase resetting dynamics. According to this model, the dynamical characteristics of neural networks are studied in three coupling cases, namely, series and parallel coupling, series coupling, and unilateral coupling. The results show that the indentified structure of neural networks enables the basic characteristics of neural information processing to be described in terms of the actions of both the optional motor and the reflected motor. The excitation of local neural networks is caused by the action of the optional motor. In particular, the excitation of the neural population caused by the action of the optional motor in the motor cortex is larger than that caused by the action of the reflected motor. This phenomenon indicates that there are more neurons participating in the neural information processing and the excited synchronization motion under the action of the optional motor.     

Generalized synchronization of spatiotemporal chaos in a weighted complex network

The nodes of the network are composed of the spatiotemporal chaos systems. The relations between the nodes are built through a weighted connection and the nonlinear terms of the chaos systems themselves are taken as coupling functions. The structure of the coupling functions between the connected nodes and the range of the control gain are obtained based on Lyapunov stability theory. It is proven that generalized chaos synchronization of the weight complex network can be realized even if the coupling strength between the nodes is adopted as any weight value. Subsequently, the catalytic reaction diffusion system which has spatiotemporal chaos behavior is taken as example, and simulation results show the effectiveness of the synchronization principle.     

Multiple synchronization transitions due to periodic coupling strength in delayed Newman–Watts networks of chaotic bursting neurons

In this paper, we numerically study the effect of time-periodic coupling strength on the synchronization of firing activity in delayed Newman–Watts networks of chaotic bursting neurons. We first examine how the firing synchronization transitions induced by time delay under fixed coupling strength changes in the presence of time-periodic coupling strength, and then focus on how time-periodic coupling strength induces synchronization transitions in the networks. It is found that time delay can induce more synchronization transitions in the presence of time-periodic coupling strength compared to fixed coupling strength. As the frequency of time-periodic coupling strength is varied, the firing exhibits multiple synchronization transitions between spiking antiphase synchronization and in-phase synchronization of various firing behaviors including bursting, spiking, and both bursting and spiking, depending on the values of time delay. These results show that time-periodic coupling strength can increase the synchronization transitions by time delay and can induce multiple synchronization transitions of various firing behaviors in the neuronal networks. This means that time-periodic coupling strength plays an important role in the information processing and transmission in neural systems.     

时滞耦合系统非线性动力学的研究进展

随着对自然界客观规律的深入认识,工程系统设计的精细化和复杂性要求也与日剧增.在许多耦合的动态系统设计过程中要考虑由耦合过程的时滞所引发的动力学行为,该时滞来自于与传感系统、作动系统和控制系统耦合的过程.耦合时滞也广泛存在于交通、系统生物学、电子通讯、神经和信息网络等技术中.本文首先从耦合时滞出发,在以时滞为中心的耦合系统复杂动力学机制、时滞镇定耦合系统的实验基础和实现、快慢变时滞耦合系统动力学和时滞神经网络同步和去同步4个方面,对耦合时滞诱发的动力学研究进展进行综述.着重介绍了时滞耦合系统中耦合时滞诱发的高余维分岔奇异性及新的定量分析方法、中立型时滞微分方程的规范型计算、具有耦合时滞的非线性系统中耦合时滞和非线性参数的辨识方法与实验实现、快慢变时滞耦合系统的张弛振荡、耦合时滞诱发的网络系统的同步模式切换等问题的研究进展;然后在应用方面重点介绍了车床磨削加工过程中耦合时滞诱发的颤振及其机理、具有惯性项和耦合时滞的神经网络系统中耦合时滞诱发的高余维分岔和复杂动力学、时滞动力吸振器与隔振装置的设计与实验实现.最后,从耦合时滞系统的一般性理论和工程应用两个方面展望了近期值得关注的一些问题.     

Study on spatiotemporal chaos synchronization among complex networks with diverse structures

The spatiotemporal chaos synchronization among complex networks with diverse structures is investigated. The spatiotemporal chaos systems are taken as the nodes of networks and constructed as some networks with diverse structures. The conditions of global synchronization among networks and the coupling function to be determined among diverse networks are discussed and confirmed based on stability theory. The Burgers equation with many practice physics processes, such as turbulent flow and heat-transfer, is adopted for example to imitate the experiment. It is found that the synchronization performance among all networks is very stable.